Power Efficiency, Overhead, and Complexity Tradeoff of IRS Codebook Design – Quadratic Phase-Shift Profile

Vahid Jamali, Marzieh Najafi, Robert Schober, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review


In this paper, we focus on large intelligent reflecting surfaces (IRSs) and propose a new codebook construction method to obtain a set of predesigned phase-shift configurations for the IRS unit cells. Since the overhead for channel estimation and the complexity of online optimization for IRS-assisted communications scale with the size of the phase-shift codebook, the design of small codebooks is of high importance. We show that there exists a fundamental tradeoff between power efficiency and the size of the codebook. We first analyze this tradeoff for baseline designs that employ a linear phase-shift across the IRS. Subsequently, we show that an efficient design for small codebooks mandates higher-order phase-shift variations across the IRS. Consequently, we propose a quadratic phase-shift design, derive its coefficients as a function of the codebook size, and analyze its performance. Our simulation results show that the proposed design yields a higher power efficiency for small codebooks than the linear baseline designs.

Original languageEnglish (US)
JournalIEEE Communications Letters
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Channel estimation
  • Complexity theory
  • Discrete Fourier transforms
  • Downlink
  • Intelligent reflecting surfaces
  • Millimeter wave communication
  • Optimization
  • Transmission line matrix methods
  • and power efficiency
  • channel estimation overhead
  • complexity
  • phase-shift design

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